Using Blender Game Engine for VR 360 tour on Mobile, is it doable?
Blender Game Engine only runs on Windows Mac and Linux, not on mobile platforms like iOS or Android. And even then, in desktop OSs it is often regarded as an aging and limited game engine, needing a long overdue overhaul, when compared to more modern solutions out there.

It will in fact be retired as of version 2.80 going forward, and it is will not receive further official development.

There was an experimental BGE APK version running on Android but it is just a proof of concept, very feature limited and not actively maintained. Also it certainly predates the emergence of modern VR so I wouldn't expect it to support anything of the kind at all.

You could probably use Blender in your pipeline for asset and environment production but I wouldn't rely on it as a lasting game engine solution, and certainly never for mobile platforms.

You could alternatively use any of the well know solutions out there like Unity or Unreal, or perhaps look into WebGL for a more universal browser based solution.

There is also the Blend4Web plugin for Blender which now supports browser based Virtual Reality through the WebVR API, even on mobile platforms. It has a full GUI inside Blender for most basic functionality from creation of assets, materials, animations, to basic interaction logic.